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LekaFEV [45]
3 years ago
7

In ∆ABC with m∠C = 90° the sides satisfy the ratio BC:AC:AB = 4:3:5. If the side with middle length is 12 cm, find: 1) The perim

eter of ∆ABC; 2) The area of ∆ABC; 3) The height to the hypotenuse.
Mathematics
2 answers:
olga55 [171]3 years ago
8 0
*The side with the middle length is 12cm, therefore BC must be 12 cm

------------------------------------------------------------<span>
Ratio 
------------------------</span>---------------------------------<span>--
BC:AC:AB
  4 : 3 : 5

</span>-----------------------------------------------------------
<span>Find 1 share
</span>-----------------------------------------------------------<span>
Given that BC = 12 cm
4 shares = 12 cm
1 share = 12 ÷ 4 = 3cm

</span>-----------------------------------------------------------
Find AC (4 shares)
-----------------------------------------------------------<span>
3 shares = 3 x 3 = 9 cm
BC = 9cm

</span>-----------------------------------------------------------
<span>Find AB (5 shares)
</span>-----------------------------------------------------------<span>
5 shares = 5 x 3 = 15cm
AB = 15cm

</span>------------------------------------------------------------
Length
-----------------------------------------------------------
   BC   :  AC   :  AB
12cm  :  9cm : 15cm<span>

---------------------------------</span>---------------------------------<span>
Perimeter
</span>------------------------------------------------------------------
<span>12 + 9 + 15 = 36cm

</span>------------------------------------------------------------------
<span>Answer: The perimeter is 36cm
</span>------------------------------------------------------------------<span>

</span>------------------------------------------------------------------
<span>Area
</span>------------------------------------------------------------------
1/2 x 9 x 12 = 54cm²<span>

</span>------------------------------------------------------------------
Answer: Area = 54cm²
------------------------------------------------------------------<span>

Given that the biggest ratio is AB
</span>⇒AB is the hypotenuse
AB = 15 cm

------------------------------------------------------------------
Answer: Hypotenuse = AB = 15cm
------------------------------------------------------------------
kow [346]3 years ago
7 0
The Hypotenuse AB = 20cm

Hope I helped!

Let me know if you need anything else!

~ Zoe
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