Question

find the height of triangle whose base is 60cm and whose area is 600cm

Answer 1

Answer:

Correct Question :

Find the height of a trapezium when the sum of the length if whose base is 60cm and whose area is 600 cm².

$\begin{gathered}\end{gathered}$

$\begin{gathered}\end{gathered}$

Given :

↠ Base of trapezium = 60cm

↠ Area of trapezium = 600 cm²

$\begin{gathered}\end{gathered}$

To Find :

↠ Height of trapezium

$\begin{gathered}\end{gathered}$

Concept :

★ Here the concept of Area of Trapezium has been used. We are given that base of trapezium is 60 cm and area of trapezium is 600 cm.We need to find the height of trapezium.

★ So,We'll find the height of trapezium by insert the values in the required  formula.

$\begin{gathered}\end{gathered}$

Using Formula :

$\bigstar{\underline{\boxed{\bf{\red{Area_{(Trapezium)}\: =\dfrac{1}{2} \times (sum \: of \: parallel \: sides) \times height}}}}}$

$\begin{gathered}\end{gathered}$

Solution :

$\red\bigstar$ Here

↠ Area of trapezium = 600 cm

↠ Sum of parallel side (base) = 60 cm

$\red\bigstar$ Finding the height of trapezium.

${\dashrightarrow{\pmb{\sf{Area_{(Trapezium)}\: =\dfrac{1}{2} \times (sum \: of \: parallel \: sides) \times height}}}}$

Substuting the values

${\dashrightarrow{\sf{600 =\dfrac{1}{2} \times60 \times height}}}$

${\dashrightarrow{\sf{600 =\dfrac{1 \times 60}{2} \times height}}}$

${\dashrightarrow{\sf{600 =\dfrac{60}{2} \times height}}}$

${\dashrightarrow{\sf{600 = \cancel\dfrac{60}{2} \times height}}}$

${\dashrightarrow{\sf{600 =30 \times height}}}$

${\dashrightarrow{\sf{Height_{(Trapezium)} = \dfrac{600}{30} }}}$

${\dashrightarrow{\sf{{Height_{(Trapezium)}=\cancel\dfrac{600}{30}}}}}$

${\dashrightarrow{\sf{Height_{(Trapezium)}\: = 20 \: cm }}}$

${\bigstar{\underline{\boxed{\bf{\purple{Height_{(Trapezium)}= 20 \: cm }}}}}}$

∴ Height of trapezium is 20 cm.

$\begin{gathered}\end{gathered}$

Verification :

$\red\bigstar$ Let's check our answer

${\dashrightarrow{\pmb{\sf{Area_{(Trapezium)}\: =\dfrac{1}{2} \times (sum \: of \: parallel \: sides) \times height}}}}$

Substuting the values

${\dashrightarrow{\sf{600 \: {cm}^{2} =\dfrac{1}{2} \times (60) \times 20}}}$

${\dashrightarrow{\sf{600 \: {cm}^{2} =\dfrac{1 \times 60 \times 20}{2}}}}$

${\dashrightarrow{\sf{600 \: {cm}^{2} =\dfrac{1200}{2}}}}$

${\dashrightarrow{\sf{600 \: {cm}^{2} = \cancel\dfrac{1200}{2}}}}$

${\dashrightarrow{\sf{600 \: {cm}^{2} =600 \: {cm}^{2} }}}$

${\bigstar{\underline{\boxed{\bf{\purple{LHS = RHS }}}}}}$

∴ Hence Verified!.

$\begin{gathered}\end{gathered}$

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Answer 2

Answer:

Hence, height / Altitude of triangle will be 20 cm

Step-by-step explanation:

In context to question asked,

We have to determine the altitude / Height of triangle.

As per data given in the question,

We have,

Area of triangle = 600 Sq. cm

Base of triangle = 60 cm

As we know that,

Triangle is a three sided figure,

Sum of all angles of the triangle is 180 degree.

The area of triangle can be determined by using formula $Area = \frac{1}{2} \times base \times Height$

So, for determining the height of triangle we will put the value of base and area given in the question in above formula,

Thus we will get it as,

$Area =\frac{1}{2} \times b \times h\\=>600 = \frac{1}{2}\times 60 \times h\\=>h = \frac{600 \times 2}{60}\\=>h = 10\times 2 = 20\:cm$