Question

1. the diagonal of a rectangle is 25 in. the width is 15 inches. what is the length?

two sides of a right triangle are 8 and 12. find the hypotenuse.

Explanation:

Problem 5:

Step1: Recall Pythagorean theorem

For a rectangle, the diagonal forms a right triangle with length (\(l\)) and width (\(w\)). The Pythagorean theorem is \(d^{2}=l^{2}+w^{2}\), where \(d\) is the diagonal. We need to solve for \(l\), so \(l = \sqrt{d^{2}-w^{2}}\).

Step2: Substitute values

Given \(d = 25\) in and \(w = 15\) in. Substitute into the formula: \(l=\sqrt{25^{2}-15^{2}}=\sqrt{625 - 225}=\sqrt{400}\).

Step3: Simplify the square root

\(\sqrt{400}=20\).

Step1: Recall Pythagorean theorem

For a right triangle, \(c^{2}=a^{2}+b^{2}\), where \(c\) is the hypotenuse and \(a\), \(b\) are the legs. Here, \(a = 8\) and \(b = 12\).

Step2: Substitute values

\(c=\sqrt{8^{2}+12^{2}}=\sqrt{64 + 144}=\sqrt{208}\).

Step3: Simplify the square root

\(\sqrt{208}=\sqrt{16\times13}=4\sqrt{13}\approx14.42\) (if decimal approximation is needed, or leave as \(4\sqrt{13}\)).

Answer:

20 inches

Next Problem (Finding hypotenuse of right triangle with sides 8 and 12):