Question

Find the height of a triangle having an area of 175 cm and base 25 cm​

Answer 1

Given -

• Area of triangle = 175cm²

• Base of triangle = 25cm

To find -

• Height of the triangle.

Formula used -

• Area of triangle

Solution -

In the Question, we are provided with the base and the area of a triangle and we need to find it's height, for that, we will consider height as h, then we will apply the formula of area of Triangle, after that we will solve the further question.

According to question -

• Area of Triangle (a) = 175cm²

• Base of triangle (b) = 25cm

• Height of triangle = h

Area of Triangle -

$\sf \dfrac{1}{2} \: \times \: base \: \times \: height$

On substituting the values -

$\sf \longrightarrow \: a \: = \dfrac{1}{2} \: \times \: b \: \times \: h \\ \\ \sf \longrightarrow \: 175 {cm}^{2} = \dfrac{1}{2} \: \times \: 25cm \: \times \: h \\ \\ \sf \: \ \longrightarrow175 {cm}^{2} = 2 \: \times 25cm \: \times \: h \\ \\ \sf \longrightarrow 175 {cm}^{2} = 50 \: \times h \\ \\ \sf \longrightarrow \: h \: = \cancel\dfrac{175}{50} \\ \\ \sf \longrightarrow \: h = 3.5cm$

Verification -

$\sf \longrightarrow \: 175 {cm}^{2} = \dfrac{1}{2} \: \times 25cm \: \times 3.5cm \\ \\ \sf \longrightarrow \: 175 {cm}^{2} = 50cm \: \times \: 3.5cm \\ \\ \longrightarrow \: \sf 175 {cm}^{2} = 175 {cm}^{2}$

$\therefore$ The height of the triangle is 3.5cm

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Answer 2

Step-by-step explanation:

★ Concept :-

Here the concept of Area of Triangle has been used. As we see, that we are given the area and the base of the triangle. We need to find the height of the triangle. So firstly we will take the height of the triangle as "h". After that, by applying the required values in the formula of Area of Triangle we will get the answer.

Let's do it !!!

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★ Formula Used :-

$\star\;\underline{\boxed{\sf{\pink{Area\ of\ Triangle\ =\ \bf \dfrac{1}{2} \times base \times height.}}}}$

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★ Solution :-

Given,

↬ Area of Triangle = 175cm².

↬ Base of Triangle = 25cm.

• Let the height of the Triangle be "h" cm.

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~ For the height of triangle ::

We know that,

$\sf \mapsto {Area\ of\ Triangle\ =\ \bf \dfrac{1}{2} \times base \times height}$

⦾ By applying the values, we get :-

$\sf \mapsto {Area\ of\ Triangle\ =\ \bf \dfrac{1}{2} \times base \times height}$

$\sf \mapsto {175cm^2\ =\ \bf \dfrac{1}{2} \times 25cm \times h}$

$\sf \mapsto {175cm^2\ =\ \bf 2 \times 25 \times h}$

$\sf \mapsto {175cm^2\ =\ \bf 50 \times h}$

$\sf \mapsto {h\ =\ \bf \cancel \dfrac{175}{50}}$

$\bf \mapsto {Height,\ h\ =\ {\red {3.5cm.}}}$

∴ Hence, height of triangle = 3.5cm.

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$\begin{gathered} \small\boxed { \begin{array} {cc} \large\bf\dag\: {\underline{More\ to\ know}} \\ \\ \\ \bf \bigstar {The\ sum\ of\ all\ three\ angles\ of\ Triangle\ is\ 180^{\circ}.} \\ \\ \\ \bf \bigstar {Area\ of\ Traingle\ =\ \dfrac{1}{2} \times base \times height.} \\ \\ \\ \bf \bigstar {Perimeter\ of\ Triangle\ =\ Sum\ of\ all\ three\ sides.} \end{array} } \end{gathered}$