Please help on timerr

Mathematics

1 answer:

rewona [7]2 years ago

3 0

the answer would be -6

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Please help?!

Anton [14]

Answer:

Δ PQT ~ Δ QRS .....{S-S-S test for similarity}...Proof is below.

Step-by-step explanation:

Given:

In Δ PQT

PQ = 30 ft

QT = 28 ft

TP = 20 ft

In Δ QRS

QR = 15 ft

RS = 14 ft

SQ = 10 ft

To Prove:

Δ PQT ~ Δ QRS

Proof:

First we consider the ratio of the sides

$\frac{PQ}{QR}=\frac{30}{15} = \frac{2}{1}$ ..............( 1 )

$\frac{QT}{RS}=\frac{28}{14} = \frac{2}{1}$ ..............( 2 )

$\frac{TP}{SQ}=\frac{20}{10} = \frac{2}{1}$ ..............( 3 )

So By equation ( 1 ), ( 2 ) and ( 3 ) we get

$\frac{PQ}{QR}=\frac{QT}{RS} = \frac{TP}{SQ}$

Now in Δ PQT and Δ QRS we have

$\frac{PQ}{QR}=\frac{QT}{RS} = \frac{TP}{SQ}$

Which are corresponding sides of a similar triangle in proportion.

∴ Δ PQT ~ Δ QRS .....{S-S-S test for similarity}...Proved

8 0

3 years ago

Help me. I don't understand. Please help me find X and IK

sertanlavr [38]

Answer:

$x=4\\\\y=6\\\\IK=47$

Step-by-step explanation:

Two Tangent Theorem: Tangents which meet at same point are equal in length.

Here tangents at J and H meet at I.

$Hence\ HI=IJ\\\\y^2-10=4y+2\\\\y^2-4y-12=0\\\\y^2-6y+2y-12=0\\\\y(y-6)+2(y-6)=0\\\\(y-6)(y+2)\\\\y\ can\ not\ be\ negative\ as\ in\ that\ case\ IJ\ will\ be\ negative.\\\\Hence\ y=6\\\\IJ=4y+2=4\times 6+2=26\\\\\\\\Tangents\ at\ J\ and\ L\ meet\ at\ K.\ Use\ two\ tangent\ theorem.\\\\JK=KL\\\\5x+1=6x-3\\\\6x-5x=1+3\\\\x=4\\\\JK=5x+1=5\times 4+1=21\\\\\\IK=IJ+JK=26+21\\\\IK=47$