Question

find the altuide of a tringle whose is 15 cm and area is 0.9
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Answer 1

Correct Question -

Find the altitude of a triangle whose base is 15 cm and area is 0.9cm²

Given -

• Area of triangle = 0.9cm²

• Base of triangle = 15cm

To find -

• Altitude of the triangle.

Solution -

In the question, we are provided with the base and the area of a triangle, and we need to find the altitude of the triangle. For that we will use the formula of area of triangle, first we will term altitude as a, then we will use the formula of area of triangle, from that we will find altitude. Let's do it!

So -

Area of triangle = $\sf\dfrac{1}{2}$ × Base × altitude

On substituting the values -

Area = 1/2 × base × altitude

$\longrightarrow \sf0.9{cm}^{2} = \dfrac{1}{2} \times 15cm \times a \\ \\ \\ \sf \longrightarrow \: 0.9 {cm}^{2} = \frac{2}{15} \times a \\ \\ \\ \longrightarrow \sf \: a = 0.9 \times \frac{2}{15} \\ \\ \\ \longrightarrow \sf \: a = \frac{1.8}{15} \\ \\ \\ \longrightarrow \sf \: a = 0.12cm$

$\therefore$ Altitude of the triangle is 0.12cm

Verification -

Area = 1/2 × base × altitude

0.9cm² = 1/2 × 15cm × 0.12cm

0.9cm² = 0.9cm²

Hence, verified

________________________________________________

Answer 2

${\large{\bold{\sf{\underbrace{\underline{Let's \; understand \; the \; question \; 1^{st}}}}}}}$

${\longmapsto}$ This question says that we have to find altitude of triangle whose area is 0.9 cm² and base is 15 cm. Altitude means height.

$\: \: \: \: \: \:{\large{\bold{\sf{\underline{Given \; that}}}}}$

${\longmapsto}$ Base of triangle = 15 cm

${\longmapsto}$ Area of triangle = 0.9 cm²

$\: \: \: \: \: \:{\large{\bold{\sf{\underline{To \; find}}}}}$

${\longmapsto}$ Altitude or height of triangle

$\: \: \: \: \: \:{\large{\bold{\sf{\underline{Solution}}}}}$

${\longmapsto}$ Altitude or height of triangle = 0.12 cm

$\: \: \: \: \: \:{\large{\bold{\sf{\underline{Using \; concept}}}}}$

${\sf{\longmapsto Area \: of \: triangle \: formula}}$

$\: \: \: \: \: \:{\large{\bold{\sf{\underline{Using \; formula}}}}}$

${\sf{\longmapsto Area \: of \: triangle \: = \: \dfrac{1}{2} \times Base \times Height}}$

$\: \: \: \: \: \:{\large{\bold{\sf{\underline{Full \; Solution}}}}}$

$\: \: \: \:{\sf{\longmapsto Area \: of \: triangle \: = \: \dfrac{1}{2} \times B \times H}}$

Where,

➝ B means Base

➝ H means Height

$\: \: \: \:{\sf{\longmapsto 0.9 \: = \dfrac{1}{2} \times 15 \times H}}$

$\: \: \: \:{\sf{\longmapsto 0.9 \: = 1 \times 7.5 \times H}}$

$\: \: \: \:{\sf{\longmapsto 0.9 \: = 7.5 \times H}}$

$\: \: \: \:{\sf{\longmapsto \dfrac{0.9}{7.5} = H}}$

$\: \: \: \:{\sf{\longmapsto 0.12 \: cm = H}}$

$\: \: \: \:{\sf{\longmapsto H = 0.12 \: cm}}$

${\green{\frak{Henceforth, \: 0.12 \: cm \: is \: altitude \: of \: triangle}}}$

$\rule{150}{2}$

$\: \: \: \: \: \:{\large{\bold{\sf{\underline{Let's \; verify \; it}}}}}$

$\: \: \: \:{\sf{\longmapsto Area \: of \: triangle \: = \: \dfrac{1}{2} \times B \times H}}$

$\: \: \: \:{\sf{\longmapsto 0.9 \: = \: \dfrac{1}{2} \times 15 \times 0.12}}$

$\: \: \: \:{\sf{\longmapsto 0.9 \: = \: 0.9}}$

$\: \: \: \:{\sf{\longmapsto L.H.S \: = \: R.H.S}}$

$\: \: \: \: \: \: \: \: \:{\sf{\purple{\dag{Hence, \; verified}}}}$

$\rule{150}{2}$

${\large{\bold{\sf{\underbrace{\underline{More \; knowledge}}}}}}$

Triangle diagram -

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)(3,3)\qbezier(5,0)(5,0)(3,3)\qbezier(5,0)(1,0)(1,0)\put(2.85,3.2){ \bf A }\put(0.5,-0.3){ \bf C }\put(5.2,-0.3){ \bf B }\end{picture}$

Right angle Triangle diagram -

$\setlength{\unitlength}{1cm}\begin{picture}(6,5)\linethickness{.4mm}\put(1,1){\line(1,0){4.5}}\put(1,1){\line(0,1){3.5}}\qbezier(1,4.5)(1,4.5)(5.5,1)\put(.3,2.5){\large\bf a}\put(2.8,.3){\large\bf 2a}\put(1.02,1.02){\framebox(0.3,0.3)}\put(.7,4.8){\large\bf A}\put(.8,.3){\large\bf B}\put(5.8,.3){\large\bf C}\qbezier(4.5,1)(4.3,1.25)(4.6,1.7)\put(3.8,1.3){\large\bf \Theta }\end{picture}$

Diagram of this question -

See from the attachment please

$\rule{150}{2}$

Request -

• Kindly see this answer from web browser or chrome just saying because I give some diagrams here but they are not shown in app. Thank you.