{"id":39834,"date":"2025-06-27T10:12:42","date_gmt":"2025-06-27T10:12:42","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=39834"},"modified":"2025-06-27T10:12:43","modified_gmt":"2025-06-27T10:12:43","slug":"a-rectangle-has-an-area-of-x2-17x-72-square-units","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/a-rectangle-has-an-area-of-x2-17x-72-square-units\/","title":{"rendered":"A rectangle has an area of (x^2 – 17x + 72) square units."},"content":{"rendered":"\n

A rectangle has an area of (x^2 – 17x + 72) square units. Since the area of a rectangle is determined using the formula, A = lw, what could be the length and width of the rectangle<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To find the possible length and width of a rectangle with an area of x2\u221217x+72x^2 – 17x + 72×2\u221217x+72 square units, we need to factor the given quadratic expression. The area of a rectangle is given by the formula:A=l\u00d7wA = l \\times wA=l\u00d7w<\/p>\n\n\n\n

So, we want to express the area x2\u221217x+72x^2 – 17x + 72×2\u221217x+72 as a product of two binomials, which will represent the possible length and width of the rectangle.<\/p>\n\n\n\n

Step 1: Factor the quadratic expression<\/h3>\n\n\n\n

We are given:x2\u221217x+72x^2 – 17x + 72×2\u221217x+72<\/p>\n\n\n\n

We need two numbers that multiply to 72 and add to -17. These numbers are -9 and -8 because:\u22129\u00d7\u22128=72and\u22129+(\u22128)=\u221217-9 \\times -8 = 72 \\quad \\text{and} \\quad -9 + (-8) = -17\u22129\u00d7\u22128=72and\u22129+(\u22128)=\u221217<\/p>\n\n\n\n

So we factor the expression:x2\u221217x+72=(x\u22129)(x\u22128)x^2 – 17x + 72 = (x – 9)(x – 8)x2\u221217x+72=(x\u22129)(x\u22128)<\/p>\n\n\n\n

Step 2: Interpret the factors<\/h3>\n\n\n\n

Now that we have factored the expression, the area becomes:A=(x\u22129)(x\u22128)A = (x – 9)(x – 8)A=(x\u22129)(x\u22128)<\/p>\n\n\n\n

This means the rectangle could have a length of (x – 9)<\/strong> units and a width of (x – 8)<\/strong> units, or vice versa.<\/p>\n\n\n\n

\n\n\n\n

Explanation<\/h3>\n\n\n\n

Factoring quadratic expressions helps us determine dimensions that, when multiplied, result in the original expression. In this case, since the area of the rectangle is given as x2\u221217x+72x^2 – 17x + 72×2\u221217x+72, we look for two binomials whose product equals the area. Factoring reveals that (x\u22129)(x\u22128)(x – 9)(x – 8)(x\u22129)(x\u22128) is equivalent to x2\u221217x+72x^2 – 17x + 72×2\u221217x+72. These two expressions represent potential measurements of the rectangle.<\/p>\n\n\n\n

The reason we factor is because the formula for the area of a rectangle is based on multiplication. To reverse that operation and find possible dimensions, we use factoring. Understanding this connection between algebraic expressions and geometric shapes helps bridge abstract and real-world problem solving. This also reinforces the concept that different binomial factors can represent dimensions of a shape while maintaining the same total area.<\/p>\n\n\n\n

\"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

A rectangle has an area of (x^2 – 17x + 72) square units. Since the area of a rectangle is determined using the formula, A = lw, what could be the length and width of the rectangle The Correct Answer and Explanation is: To find the possible length and width of a rectangle with an […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-39834","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/39834","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=39834"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/39834\/revisions"}],"predecessor-version":[{"id":39844,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/39834\/revisions\/39844"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=39834"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=39834"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=39834"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}