Question

The are of a rhombus is 119cm square and it's perimeter is 56 cm. Find the altitude

Answer 1

Step-by-step explanation:

ar. = ½×d¹×d²

=> 119cm²= ½d¹d²

=> d¹×d²= 238 cm²

Now ; p= 4s

=> 56=4s

=> s= 14 cm

and, diagonals bisect at 90°

=> in any ∆ , we have :

(d¹/2)²+(d²/2)²= s²

=> d¹^²+d²^²= 196× 4 = 784 cm

Now; (d¹+d²)²

= d¹^²+d²^²+2d¹d²

= 784+ 476

= 1260

Thus ,

√1260= d¹+d²

=> d¹+d²= √ 3×5×7×2×3×2

=> d¹+d²= 6√35 cm

So sum of both altitudes = (d¹+d²)÷2 =3√35 cm

Calculate the rest value of each altitude by finding each diagonal and dividing it by two.

Hope it helps!