One of the diagonals of a rectangle is 20 cm long. If the difference between its length and width is 4 cm, then find the area of the rectangle.
Answers
★SOLUTION★
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Let x be the length of the rectangle.
Because the difference between its length and width is 4 cm, its width must be either (x + 4) cm or (x - 4) cm.
Let's take the width as (x + 4) cm.
In the right triangle, according to Pythagorean theorem, we have
(x + 4)² + x2 = 202
Simplify.
x² + 2(x)(4) + 42 + x2 = 400
x² + 8x + 16 + x2 = 400
2x² + 8x + 16 = 400
Subtract 400 from each side.
2x² + 8x - 384 = 0
Divide each side by 2.
x² + 4x - 192 = 0
(x + 16)(x - 12) = 0
x + 16 = 0 or x - 12 = 0
x = -16 or x = 12
Because the length of a rectangle can never be a negative value, we can ignore x = -16.
So, the value of x is 12.
Then,
x + 4 = 12 + 4
x + 4 = 16
Therefore,
length = 12 cm
width = 16 cm
Area of the triangle :
= l × b
= 12 × 16
= 192 cm²
So, the area of the rectangle is 192 square cm.
Step-by-step explanation:
rectangle is 20 cm long is the difference between IS and it is 4 cm find the area of rectangle