# a rectangle is 7cm longer than it is wide. The diagonal is 13 cm. What are the rectangle's dimensions?

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- 9 years agoFavorite Answer
Half of a rectangle is a right triangle, so you can use pythagoreans theorem.The diagonal will be the side opposite of the right angle (c).

a^2 + b^2 = c^2

say a is width and b is length.

b = 7 + a since the rectangle is 7 cm longer than it is wide

rearranging you get:

a^2 + (7 + a)^2 = 13^2

a^2 + 49 + 14a + a^2 = 169

2(a^2) + 14 a - 120 = 0

divide everything by 2:

a^2 + 7a - 60 = 0

factor:

(a + 12)(a - 5) = 0

so a = 5 or - 12

since dimensions can't be negative, a = 5

thus b = 5 + 7 = 12

so the length is 12 cm and the width is 5 cm

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