Question

question 2 points 3
the length of a rectangular poster is 9 inches longer than its width. if the diagonal is 15 inches, what are the dimensions of the poster?

○ 6.201 inches by 15.20 inches

○ 5.105 inches by 14.105 inches

○ 6.105 inches by 13.105 inches

○ 14.12 inches by 15.13 inches

Explanation:

Step1: Define variables

Let the width of the poster be \( x \) inches. Then the length is \( x + 9 \) inches.

Step2: Apply Pythagorean theorem

For a rectangle, the diagonal \( d \) satisfies \( d^{2}=x^{2}+(x + 9)^{2}\). Given \( d = 15 \), we have:

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Step3: Solve quadratic equation

Using the quadratic formula \( x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a} \) for \( ax^{2}+bx + c = 0 \). Here, \( a = 1 \), \( b = 9 \), \( c=-72 \):

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We take the positive root: \( x=\frac{-9 + 19.209}{2}=\frac{10.209}{2}=5.1045\approx5.105 \). Then the length is \( 5.105+9 = 14.105 \) inches.

Answer:

5.105 inches by 14.105 inches (the second option)