Question

4. A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26 cm, 29 cm and 30 cm and the parallelogram stands on the base 28 cm, find the height of the parallelogram.​

Answer 1

Answer:

Let ABC be a triangle with sides

AB = 26 cm, BC = 28 cm, CA = 30 cm

Now, s=AB+BC+CA2

=(26+28+302)cm

⇒s=842cm

⇒s=42cm

Area of ΔABC=42(42−26)(42−28)(42−30)−−−−−−−−−−−−−−−−−−−−−−−−√

=42×16×14×12−−−−−−−−−−−−−−√   (by Heron's formula)

=7×2×3×2×2×2×2×7×2×3×2×2−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−√

=7×2×2×2×2×3

=336cm2

We know that, area of parallelogram = base × height   ...(1)

We have, area of parallelogram = area of ΔABC (given)

=336cm2

From eq. (1), we have

base × height = 336

⇒28× height = 336

⇒height=33628

⇒height=12cm

Step-by-step explanation:

i think it useful to you

Answer 2

Perimeter of Triangle

2S=26+28+30=84

⇒S=42cm

Area

√s(s−a)(s−b)(s−c) (Heron's formula)

Area =

√42(42−26)(42−28)(42−30) = √42×16×14×12

Area=336cm²

Area of parallelogram = Area of triangle

⇒ h×28=336

⇒h=12cm

Height of parallelogram =12cm

hope it will help you.