Question

Find the altitude of a rhombus whose area is 420 cm(sq) and perimeter is 140 cm

Answer 1

rhombus has all sides equal so it's each side is 140/4=35
now area of rhombus is base *altitude
so
35*altitude=420
altitude=12

Answer 2

Area of a rhombus = 420 sq.cm
Its perimeter = 140 cm
Measure of each of its sides= 140/4 cm = 35 cm

Now, ABCD be the rhombus.
Then,
Area of triangle ABD + Area of triangle BCD = Area of the rhombus ABCD
let the height be h.
Then,
$\frac{1}{2} \times 35 \times h + \frac{1}{2} \times 35 \times h = 420 \\ 2( \frac{1}{2} \times 35 \times h) = 420 \\ \frac{1}{2} \times 35 \times h = \: \frac{420}{2} \\ \frac{1}{2} \times 35 \times h = 210 \\ h = 210 \times \frac{2}{35 } \\ h = 12cm$
hope it helps