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Brrunno [24]
3 years ago
5

If M is the centroid of triangle GHI, HL=45, JI=63, and KG=60, find the missing measures

Mathematics
1 answer:
AysviL [449]3 years ago
6 0

Answer:

Part a) ML=15\ units

Part b) HM=30\ units

Part c) JM=21\ units

Part d) MI=42\ units

Part e) GM=40\ units

Part f) MK=20\ units

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

A <u><em>centroid</em></u> of a triangle is the point where the three medians of the triangle meet. A median of a triangle is a line segment from one vertex to the mid point on the opposite side of the triangle.

The centroid is located two thirds of the distance from any vertex of the triangle

Part a) Find ML

we have

HL=45\ units

we know that

ML=\frac{1}{3}HL

substitute the given value

ML=\frac{1}{3}(45)

ML=15\ units

Part b) Find HM

we have

HL=45\ units

we know that

HM=\frac{2}{3}HL

substitute the given value

HM=\frac{2}{3}(45)

HM=30\ units

Part c) Find JM

we have

JI=63\ units

we know that

JM=\frac{1}{3}JI

substitute the given value

JM=\frac{1}{3}(63)

JM=21\ units

Part d) Find MI

we have

JI=63\ units

we know that

MI=\frac{2}{3}JI

substitute the given value

MI=\frac{2}{3}(63)

MI=42\ units

Part e) Find GM

we have

KG=60\ units

we know that

GM=\frac{2}{3}KG

substitute the given value

GM=\frac{2}{3}(60)

GM=40\ units

Part f) Find MK

we have

KG=60\ units

we know that

MK=\frac{1}{3}KG

substitute the given value

MK=\frac{1}{3}(60)

MK=20\ units

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