Question

The area of a triangle is 50 cm2. If the altitude is 8cm, what is its base. *
1 point
12.5cm
12cm
13cm

Answer 1

AnswEr-:

• $\underline {\mathrm {\star{\red{The\: Measure\:Base \:of\:Triangle \:is\:12.5\:cm }}}}$

• $\underline {\mathrm {\star{\red{The\: \bf{Option \:A \:or\:12.5\:cm}\:is\:Correct . }}}}$

Explanation-:

$\sf{\bf{ Given-:}}$

• The Area of Triangle is 50 cm²

• The Altitude of Triangle is 8 cm .

$\sf{\bf{ To\:Find\:-:}}$

• The measure Base of Triangle

$\sf{\bf{\dag{ Solution \:of\:Question \:-:}}}$

• $\underbrace {\mathrm {\bf{ Understanding \:the\:Concept:-:}}}$

• We have to find the Base of Triangle when Area and Altitude of Triangle is Given.

• Firstly put the Given Values [ Area and Altitude] in the Formula for Area of Triangle.

• Now , By Doing this We can get the Base of Triangle.

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$\mathrm {\bf{\dag{ Finding \:Base \:of \:Triangle \:-:}}}$

As , We know that ,

• $\underline{\boxed{\star{\sf{\purple{ Area_{(Triangle)}  \: = \: \dfrac{1}{2} \times Altitude \times Base \:sq.units }}}}}$

$\sf{\bf{ Here-:}}$

• The Area of Triangle is 50 cm²

• The Altitude of Triangle is 8 cm .

• The Base of Triangle is ??

Now , By Putting known Values in Formula for Area of Triangle -:

• $\qquad \quad \qquad \quad \longmapsto{\mathrm { \dfrac{1}{2} \times 8 \times Base = 50 \: cm^{2} }}$

• $\qquad \quad \qquad \quad \longmapsto{\mathrm { \dfrac{1}{\cancel {2}} \times \cancel {8} \times Base = 50 \: cm^{2} }}$

• $\qquad \quad \qquad \quad \longmapsto{\mathrm { 4 \times Base = 50 \: cm^{2} }}$

• $\qquad \quad \qquad \quad \longmapsto{\mathrm { Base = \dfrac{50}{4} \: }}$

• $\qquad \quad \qquad \quad \longmapsto{\mathrm { Base = \dfrac{\cancel {50}}{\cancel {4}} \: }}$

• $\qquad \quad \qquad \quad \underline{\boxed{\pink{\mathrm { Base = 12.5 \:cm \: }}}}$

Hence ,

• $\underline {\mathrm {\star{\red{The\: Measure\:Base \:of\:Triangle \:is\:12.5\:cm }}}}$

• $\underline {\mathrm {\star{\red{The\: \bf{Option \:A \:or\:12.5\:cm}\:is\:Correct . }}}}$

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$\Large {\mathrm {Verification \:\red{♡}-:}}$

As , We know that ,

• $\underline{\boxed{\star{\sf{\purple{ Area_{(Triangle)}  \: = \: \dfrac{1}{2} \times Altitude \times Base \:sq.units }}}}}$

$\sf{\bf{ Here-:}}$

• The Area of Triangle is 50 cm²

• The Altitude of Triangle is 8 cm .

• The Base of Triangle is 12.5 cm .

Now , By Putting known Values in Formula for Area of Triangle -:

• $\qquad \quad \qquad \quad \longmapsto{\mathrm { \dfrac{1}{2} \times 8 \times 12.5 = 50 \: cm^{2} }}$

• $\qquad \quad \qquad \quad \longmapsto{\mathrm { \dfrac{1}{\cancel {2}} \times \cancel {8} \times 12.5 = 50 \: cm^{2} }}$

• $\qquad \quad \qquad \quad \longmapsto{\mathrm { 4 \times 12.5 = 50 \: cm^{2} }}$

• $\qquad \quad \qquad \quad \underline{\boxed{\pink{\mathrm { 50cm^{2} = 50 \:cm^{2} \: }}}}$

Therefore,

• $\qquad \quad \qquad \quad:\implies {\mathrm { L.H.S = R.H.S }}$

• $\qquad \quad \qquad \quad:\implies {\mathrm { Hence \:, Verified \:! }}$

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$\large { \boxed {\mathrm |\:\:{\underline {More \:To\:Know\:-:}}\:\:|}}$

• Area of Rectangle = Length × Breadth sq.units

• Area of Square = Side × Side sq.units

• Area of Triangle = ½ × Base × Height sq.units

• Area of Trapezium = ½ × Height × ( a +b ) or Sum of Parallel sides sq.units

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Answer 2

$\Huge{\mathfrak{\blue{\underline{\red{Solution}}}}}$

Given:-

• The area of a triangle = 50$\sf{cm}^{2}$
• It's altitude is 8cm.

To Find:-

• Find the base of a triangle =?

Solution:-

Let's understand

Here, The area of triangle is given 50sqcm and it's altitude is 8cm and we have to find it's base.

Therefore,

• Area of triangle = 50$\sf{cm}^{2}$
• It's altitude is 8cm.

We know that,

$\large\sf\green{Area\:of\:triangle={\frac{1}{2}×Altitude×Base}}$

Now,Put the value

$\sf \implies \: 50 {cm}^{2} = \frac{1}{2} \times 8cm \times base \\ \\ \sf \implies \: 50 {cm}^{2} = 4cm \times base \\ \\ \sf \implies \: \frac{50}{4} = base \\ \\ \sf \implies \therefore \: base = 12.5cm$

Hence, Base of a triangle is 12.5cm.

Verification:-

$\large\sf\green{Area\:of\:triangle={\frac{1}{2}×Altitude×Base}}$

$\sf \implies \: 50 {cm}^{2} = \frac{1}{2} \times 8cm \times 12.5cm \\ \\ \sf \implies \: 50 {cm}^{2} = 50 {cm}^{2}$

LHS = RHS

Hence, Proved