Question

The area of a right-angled triangle is 30 m2. If its smallest side is 5 m, then its hypotenuse is​

Answer 1

✬ Hypotenuse = 13 cm ✬

Step-by-step explanation:

Given:

• Area of right angled triangle is 30 m².
• Measure of smallest side is 5 m.

To Find:

• What is the measure of hypotenuse ?

Solution: Let ABC be a triangle right angled at B such that

• AB = Perpendicular
• AC = Hypotenuse
• BC = Base (5 m)
• ∠ABC = 90°

Taking BC as smallest side. As we know that

★ Area of ∆ = 1/2(Base)(Height) ★

$\implies{\rm }$ Ar. of ∆ABC = 1/2(BC)(AB)

$\implies{\rm }$ 30 = 1/2 $\times$ 5 $\times$ AB

$\implies{\rm }$ 30 = 5/2 $\times$ AB

$\implies{\rm }$ 30 $\times$ 2 = 5AB

$\implies{\rm }$ 60 = 5AB

$\implies{\rm }$ 12 cm = AB

So, The measure of perpendicular of triangle is 12 cm.

Now, using Pythagoras Theorem in ∆ABC

★ Hypotenuse² = Perpendicular² + Base² ★

➙ AC² = AB² + BC²

➙ AC² = 12² + 5²

➙ AC² = 144 + 25

➙ AC² = 169

➙ AC = √169 = 13 cm

Hence, the measure of hypotenuse is 13 cm.

Answer 2

$\\ *Hypotenuse = 13 cm</p><p> \\ Step-by-step explanation:</p><p> \\ Given:</p><p> \\ Area of right angled triangle \: is 30</p><p> \\ Measure of smallest side is 5 m.</p><p> \\ To Find:</p><p> \\ What is the measure of \: hypotenuse</p><p> \\ Solution: Let ABC be a triangle \: right \: angled at B such that</p><p> \\ AB = Perpendicular</p><p> \\ AC = Hypotenuse</p><p> \\ BC - Base (5 m)</p><p> \\ ZABC = 90"</p><p> \\ Taking BC as smallest side. \\ As we know \: that \\ * Area of \\ A = 1/2(Base)(Height) *</p><p> \\ Ar. of AABC = 1/2(BC)(AB)</p><p> \\ - 30 = 1/2 x 5 x AB</p><p> \\ 30 = 5/2 x AB</p><p> \\ 30 x 2 = 5AB</p><p> \\ 60 = 5AB</p><p> \\ 12 cm = AB</p><p> \\ So, The measure of perpendicular of</p><p>triangle is 12 cm</p><p>Now, using Pythagoras Theorem in</p><p> \\ ДАВС</p><p> \\ *Hypotenuse=Perpendicular+Base</p><p> \\ → AC' = AB' + BC?</p><p> \\ → AC= 122 + 52</p><p> \\ → AC = 144 +25 \: + ACP = 169</p><p> \\ - AC = V169 = 13 cm</p><p> \\ Hence, the measure of \: hypotenuse is 13cm.$