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Xelga [282]
3 years ago
14

I’m confused on this one

Mathematics
2 answers:
Xelga [282]3 years ago
5 0
\sf Hello!

• \sf Base = 10\: ft
• \sf Height = 13\: ft

\sf Here,
\sf We\: only\: require \: Base\: and\: Height\: only.

\sf Area \: of\: Triangle :

= \dfrac{\sf 1}{\sf 2} × \sf Base × \sf Height

= \dfrac{\sf 1}{\sf 2} × \sf 10 × \sf 13

= \sf 5 × 13\: ft^{2} = \sf 65\: ft^{2}

\sf Hence,
\sf Area\: of\: the\: Triangle \: is\: 65\: ft^{2}

~ \sf iCarl
erastovalidia [21]3 years ago
4 0

In the chart of the triangle it shows that the variable b is the base. It also give us the equation for area 1/2bh (half of base * height)

Now we just plug in the values we are given

1/2bh

1/2(10*13)

1/2(130)

65

The area of the triangle is 65 ft

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Find the missing lengths: LK=15 and KH=9, find KI and HI.
Luda [366]

Answer:

KI=11.25 and HI=6.75

Step-by-step explanation:

Consider the below figure attached with this question.

According to Pythagoras Theorem:

base^2+perpendicular^2=hypotenuse^2

Use Pythagoras in triangle HKL

LH^2+KH^2=LK^2

(LH)^2+9^2=15^2

(LH)^2+81=225

(LH)^2=144

Taking square root on both sides.

LH=12

Let length of HI be x.

LI = 12+x

Use Pythagoras theorem in ΔKLI,

(KI)^2+15^2=(12+x)^2

(KI)^2+225=x^2+24x+144

(KI)^2=x^2+24x+144-225

(KI)^2=x^2+24x-81...(1)

Use Pythagoras theorem in ΔHKI,

(KI)^2=x^2+9^2

(KI)^2=x^2+81...(2)

From (1) and (2) we get

x^2+81=x^2+24x-81

24x=162

x=\dfrac{162}{24}=6.75

Hence, the measure of HI is 6.75 units.

Substitute x=6.75 in equation (2).

(KI)^2=(6.75)^2+81

(KI)^2=126.5625

Taking square root on both sides.

KI=\sqrt{126.5625}

KI=11.25

Hence, the measure of KI is 11.25 units.

3 0
3 years ago
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