The width of a rectangle is 20 cm. the diagonal is 8 cm more than the length. Find the length of the rectangle.
Created: 2 years ago |
Updated: 7 months ago
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Let's denote the length of the rectangle as "L."
According to the given information, the width of the rectangle is 20 cm, and the diagonal is 8 cm more than the length, which can be expressed as:
Diagonal = L + 8
Now, we can use the Pythagorean Theorem to relate the length, width, and diagonal of the rectangle:
Diagonal^2 = Length^2 + Width^2
Plugging in the values we have:
(L + 8)^2 = L^2 + 20^2
Expanding and simplifying:
L^2 + 16L + 64 = L^2 + 400
Now, let's solve for L:
16L + 64 = 400
Subtract 64 from both sides:
16L = 400 - 64 16L = 336
Now, divide by 16:
L = 336 / 16 L = 21
So, the length of the rectangle is 21 cm.
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