Question

Find the height of triangle whose area is 45
and base is 15 cm.​

Answer 1

$\Huge\mathfrak\purple{anSwer:}$

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$\bf{{\underline{Given}}:}$

• $\sf{Area~of~the~triangle=45cm^{2}}$
• $\sf{Base=15cm}$

$\bf{{\underline{To~find}}:}$

• $\sf{Height~of~the~triangle}$

$\bf{{\underline{Solution}}:}$

$\sf Area \: of \: a \: triangle = \frac{1}{2} \times base \times height \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf \implies {45cm}^{2} = \frac{1}{2} \times 15 \times height \\ \sf \implies \frac{1}{2} \times 15 \times height = {45cm}^{2} \\ \sf \implies \frac{1}{2} \times height = \frac{45}{15} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf \implies \frac{1}{2} \times height = 3 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf \implies height = 3 \times \frac{2}{1} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf \implies height = 3 \times 2 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf \therefore height = \purple{ \underline{ \boxed{ \bf 6cm}}} \: \: \: \: \: \: \: \: \: \:$

$\bf\therefore{{\underline{Required~answer}}:}$

• $\sf Height = \purple{ \underline{ \boxed{ \bf 6cm}}}$

Answer 2

Answer :

Given :

• Area of the triangle = 45cm²
• Base = 15cm

To find :

• Height of the triangle

Solution :

　Area of a triangle = 1/2 × base × height

→ 45cm² = 1/2 × 15cm × height

→ 1/2 × 15 × height = 45

→ 1/2 × height = 45/15

→ 1/2 × height = 3

∴ height = 3 × 2 = 6cm

∴ Required answer :

• Height of the triangle is 6cm

Verification :

　Area of a triangle = 1/2 × base × height

　　　 　　 　　　= 1/2 × 15 × 6

　　　 　　 　　　= 1/2 × 90

　　　 　　 　　　= 90/2

　　　 　　 　　　= 45cm²

• Hence verified !