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dsp73
3 years ago
8

Find the missing lengths. If needed, round the answers to the nearest tenth.

Mathematics
1 answer:
dmitriy555 [2]3 years ago
6 0

Answer:

The value of y is <u>64</u>.

The value of z is <u>225</u>.

Step-by-step explanation:

Given,

AB = 136

BC = 255

∠B = 90°

We have to find the value of 'y' and 'z'.

Solution,

Let assume D is a point on AC.

Then BD = 120

And also given ∠D = 90°

Now in ΔABD

AB = 136    and     BD = 120

∠D = 90°

So according to Pythagoras theorem;

"The square of the hypotenuse is equal to the sum of the squares of the other two sides".

AB^2=BD^2+AD^2

On substituting the values, we get;

136^2=120^2+y^2\\\\18496=14400+y^2\\\\y^2=18496-14400\\\\y^2=4096

Now taking square root on both side, we get;

\sqrt{y^2} =\sqrt{4096} \\\\y=64

Hence the value of y is 64.

Again, in ΔBDC

BC = 255    and     BD = 120

∠D = 90°

So according to Pythagoras theorem;

"The square of the hypotenuse is equal to the sum of the squares of the other two sides".

BC^2=BD^2+DC^2

On substituting the values, we get;

255^2=120^2+z^2\\\\65025=14400+z^2\\\\z^2=65025-14400\\\\z^2=50625

Now taking square root on both side, we get;

\sqrt{z^2}=\sqrt{50625}\\\\z=225

Hence the value of z is 225.

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