Question

area of a rhombus is 75 cm2 if one of the diagonal is 5 cm longer than the other find the length of both the diagonals.​

Answer 1

Answer:

I think Length of Diagonal is 10.

Answer 2

Answer:

10 cm and 15 cm

Given

$area \ of\ a\ rhombus \ is \ 75cm^{2}$

one of the diagonal is 5 cm longer than the other

Explanation:

Let the diagonal be x and x+5

We know that Area of rhombus =  ½ × d1 × d2

Where d1 and d2 are diagonals of the rhombus

$75 =\frac{x(x+5)}{2} \\\\75*2=x^{2} +5x\\\\150=x^{2} +5x\\\\x^{2} +5x-150=0\\\\x^{2} +15x-10x-150=0\\\\x(x+15)-10(x+15) =0\\(x+15)(x-10)=0\\x= -15 ,10\\\\But\ we\ know\ that\ length\ can't\ be\ negative\ so\ x\neq -15\\\\So\ x=10\\\\ Therefore\ length\ of\ diagonal =x =10 cm\\And\ x+5=10+5=15cm$

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