Question

area of a rhombus is 75 square centimetre if one of the diagonals is 5 cm longer than the other find the length of both the diagonals​

Answer 1

The length of both the diagonals​ are 10 and 15

Step-by-step explanation:

Let the diagonal 1 be x

one of the diagonals is 5 cm longer than the other

So, Diagonal 2 = x+5

Area of rhombus =$\frac{1}{2} \times d1 \times d2$

Area of rhombus = $\frac{1}{2} \times (x) \times (x+5)$

Area of a rhombus is 75 square centimeter

$\frac{1}{2} \times (x) \times (x+5)=75$

$x^2+5x=75 \times 2$

$x^2+5x-150=0$

$x^2+15x-10x-150=0$

x(x+15)-10(x+15)=0

(x-10)(x-15)=0

x=10,15

Hence  the length of both the diagonals​ are 10 and 15

#Learn more:

The side of a rhombus is 5 centimetre if the length of one diagonal of the Rhombus is it cm then find the length of the other diagonal​

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