Question

Rectangle ABCD is made by shortening one side of the square PQRS by 5cm and another by 8cm.If the area of ABCD is 180cm2 find the area of PQRS

Answer 1

Answer:

400

Step-by-step explanation:

l × b = 180

(x - 5)×(x - 8) = 180

x^2 - 8x - 5x + 40 = 180

x^2 -13x - 140 = 0

x^2 - 20x + 7x - 140 = 0

x = 20, -7 , neglect -7 length can't be -ve.

side of square = x = 20

area of PQRS = (20)^2 = 400

Answer 2

area of PQRS = 400 cm² if Rectangle ABCD is made by shortening one side of the square PQRS by 5cm and another by 8cm and area of ABCD is 180cm²

Step-by-step explanation:

Let say Area of PQRS Square =  A²

then Side of Square = A

Rectangle ABCD is made by shortening one side of the square PQRS by 5cm and another by 8cm

=> Rectangle side = A - 5  & A - 8

Area of Rectangle  = (A - 5)(A - 8)  = 180

=> A² - 13A + 40 = 180

=> A² - 13A - 140 = 0

=> A² - 20A + 7A - 140 = 0

=> A(A - 20) + 7(A - 20) =0

=> (A + 7)(A - 20) = 0

=> A = 20

A² = 20²

=> A² = 400 cm²

area of PQRS = 400 cm²

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